1.The Safari Company is currently the only company in the area that produces a line of lightweight hiking boots. Safari's advisors estimate that the demand for their boots is given by: Q = 42 -0.4 P
Where P is the average price of a boot and Q is the quantity of boots. Safari's costs are estimated with the following equation: TC = 100 + 5Q + 2.5Q2
a. Given this information, how much output should Safari's produce to maximize profits?
b. How much should it charge for each boot? Is Safari making a profit? If yes, how much?
c. Without doing any calculations, what do you predict will happen to Safari's profits if their demand decreases to Q =10-0.5P?
d. Given the new the lower demand, what can Safari do to improve its profits? Explain.
2. When producing 10 units, Fred has total variable costs of $300, total fixed costs of $150, and assets of $2000. Assume you can approximate MC with AVC.
a. If he he wants a return of 5%, what price should she charge?
b. Suppose that instead of determining price based on his target return, Fred decides to use a standard markup pricing scheme. What is the optimal markup for Tom if she estimates that the price elasticity of demand for his product is -1.5?
c. If he uses the optimal markup obtained in part b, how much should he charge for his product?
d. Given your answers to parts a and c, which pricing mechanism should he chose? How would your answer change if the price elasticity for his product increases considerably due to an increase in the availability of substitutes.
3. The Allen Corporation, a sofa retailer, wants to determine how many sofas it must sell in order to earn a profit of $15,000 per month. The price of each sofa is $500, the average variable cost is $150.
a. What is the required sales volume if fixed costs are $4000 per month?